Geoscience Reference
In-Depth Information
0.53 to 0.92 for the five discharges. The form of this relationship then suggested a modified index of
similarity as a power function of ( a tan β ). For this catchment, this resulted in a much more rapid increase
in predicted saturated area with discharge than in the unmodified model. A similar correlation and
behaviour was found later for a small humid catchment in the Jizera Mountaints of the Czech Republic
(Blazkova et al. , 2002a).
This study raises a number of interesting issues. Firstly, although we do expect from many different
field studies that the soil characteristics should be heterogeneous in space, use of local measurements
to calibrate local parameter values restricts the value of the internal data in evaluating the model.
In addition, such local calibrations of, for example, a transmissivity value should be expected to be
dependent on both model structure and model grid scale (e.g. Saulnier et al. , 1997b). Finally local
calibrations can only be made for points at which measurements are available; the Saeternbekken
MINIFELT catchment is very unusual, if not unique, in having so many internal measurement points.
Even in this very small catchment, there is the problem of extrapolating to other points in the catch-
ment. In the Lamb et al. (1997) study, this could be achieved because a suitable correlation with the
( a/ tan β ) index was found, but it cannot be concluded that this will generally be the case. In fact, such
a correlation might be an indication that there is a structural deficiency in the model formulation. The
positive correlation between apparent transmissivity and topographic index, for example, might be an
indication that the topographic analysis was overestimating the effective upslope contributing areas to
each point.
The issues are not specific to this TOPMODEL study but are generic to any application of any dis-
tributed model, including most process-based models, for which some internal data are available for
evaluation of the model predictions. One approach to model evaluation might then be a type of split
sample test in which only part of the internal data are used to test whether local parameter calibration
might be necessary and the remainder are held back to test the resulting, improved, predictions. Those
held back, however, will also have their local characteristics, implying a limit to how far such distributed
predictions can be validated. Some uncertainty in such predictions is, then, inevitable and should, if
possible, be quantified. Uncertainty in the predictions for the Saeternbekken study have been made by
Lamb et al. (1998b).
6.5 TOPKAPI
An interesting variant on the TOPMODEL approach to distribution function models is TOPographic
Kinematic Approximation and Integration - TOPKAPI (Todini, 1995; Ciarapica and Todini, 2002; Liu
and Todini, 2002). TOPKAPI attempts to account for two additional features of hillslope flow processes,
relative to the TOPMODEL approach. The first is that downslope flows in the unsaturated zone might
also contribute to the storage at any point in the catchment. By including such fluxes, the possibility
that there is no downslope saturated zone flow and very small downslope unsaturated zone effectively
allows a more dynamic formulation of the upslope contributing area to a point. Secondly, the assumption
of instantaneous redistribution of soil water storage on the hillslope, assumed for the saturated zone in
TOPMODEL, is relaxed. In TOPKAPI, an approximate relationship between downslope flux and the
integrated profile of soil moisture is assumed as:
= tan βK s α
α
q
=
(6.8)
where K s is the saturated hydraulic conductivity of the soil (assumed constant with depth), L is the depth of
the soil layer, θ is the profile integrated average relative soil moisture content ( =
L L
1
θ r )),
α is a coefficient in the Brooks-Corey relationship between relative hydraulic conductivity and moisture
( θ
θr ) / ( θ s
0
Search WWH ::




Custom Search